# Relationship between AR and MR | Explain the Relationship between Average revenue and Marginal revenue

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## Relationship between Average revenue (AR), Marginal revenue (MR) and Total revenue (TR)

These three concepts of revenues are related to each other.

Total Revenue (TR)

It refers to total receipts from the sale of a given quantity of a commodity. According to Stonier and Hague, “Total revenue at any output is equal to price per unit multiplied by quantity sold”.

Average Revenue (AR)

It refers to revenue per unit of output sold. According to economists Holland, ‘’Average revenue is the ratio of the total revenue to the quantity sold of the product”.

## Marginal Revenue (MR)

It is the additional generated from sale of an additional unit of output. In the words of Stonier and Hague, “ Marginal revenue at any level of a firm’s output is the revenue which would be earned from selling another unit of the firm’s product.

The concept of Average revenue (AR), Marginal revenue (MR) and Total revenue (TR) are explained through the following table-

 Q TR = P × Q AR = TR/Q MR = ΔTR/ΔQ Price 1 16 16 16 16 2 28 14 12 14 3 36 12 8 12 4 40 10 4 10 5 40 8 0 8 6 36 6 -4 6

In the above table shows that the TR increase with an increase in the sale of output. When 5 units are sold, the TR is maximum at Rs.40. When 6 units are sold, the TR fall to Rs.36. The table shows that AR goes on falling as the output rises. There is also a fall in MR with rise in units sold. When the 5th units is sold MR is zero (0) and when 6th units is sold MR becomes negative (-4).

The relationship between Average revenue,  Marginal revenue and Total revenue are  expressed through a diagram.

In figure (A) and (B) output is measured along the OX axis and revenues are measured along the vertical axis. In figure (A), TR starts from the origin and slops positively. Whereas 5 units are sold the TR is maximum (40). After that there is a fall in TR.

In figure (B), AR and MR are Average revenue curve and Marginal revenue curve respectively. Slope down wards from left to right and indicate that AR and MR fall as more units are sold. In case of 5th unit of output, MR becomes zero and after that it is negative.

### Relationship between AR and MR and also TR

From three revenue concepts we found following relationships-

TR = AR × Q or TR = ∑MR

AR = TR/Q = PQ/Q = P or AR = P

When AR = P is zero, TR is also zero. This is not under perfect competition.

MR = TRn - TRn -1 for an increase is Q by one unit or for continuous changes in Q.

When TR increases at the same rate, with an increase in Q, MR remains constant.

When MR is constant, it is equal to AR = P under perfect competition.

When TR is increasing at a decreasing rate, MR is declining.

When TR is maximum or constant, MR is zero.

When AR is decreasing MR falls faster than AR.

MR = P, when a firm has no control over price and MR<P when a firm has control over price.

### Conclusion

So friends, this was Explain the Relationship between Average revenue and Marginal revenue. Hope you get the full details about it and hope you like this article.

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